Denmark was actually in a pretty important position during the cold war. For one thing the Island of Bornholm is located so that it sticks the farthest into Soviet territory. Because of that Denmark had radar stations and listening stations spying on Soviet and giving intel to other NATO members.

Secondly if Russia wants to send ships out of the Baltic Sea into the Atlantic they have to go through Danish waters. Therefore Denmark acted as a gate that could be closed on Soviet ships again with radar stations and sea mines that were deployed so that we could blow up Soviet ships we didn't want passing through.

For those reasons Denmark was a really important NATO ally during the cold war, and for the same reason there were plenty of nukes pointed at us during the cold war, which we only found out later.